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"Quantum jump" is a somewhat misleading term because the transition is not instantaneous. We can assume that at any given temperature there is a characteristic length of time it takes for the system to make the transition to a distinct quantum state. A local observer's proper time is essentially counting time in terms of that characteristic interval.

As I would paraphrase the following passage: thermal time is essentially a universal version of time that reconciles and unifies all those different clocks running at different temperatures. That is what equation (4) on page 1 is saying:

τ = (kT/ħ) t

Here is the context.

==quote 1302.0724, page 1==

The core idea is to focus on histories rather than states. This is in line with the general idea that states at fixed time are not a convenient handle on general relativistic mechanics, where the notion of process, or history, turns out to be more useful [12]. Equilibrium in a stationary spacetime, namely the Tolman law, is our short-term objective, but our long-term aim is understanding equilibrium in a fully generally covariant context, where thermal energy can flow also to gravity [13–15], therefore we look for a general principle that retains its meaning also in the absence of a background spacetime.

We show in this paper that one can assign an information content to a history, and two systems are in equilibrium when their interacting histories have the same information content. In this case the net information flow vanishes, and this is a necessary condition for equilibrium. This generalized principle reduces to standard thermodynamics in the non-relativistic setting, but yields the correct relativistic generalization.

This result is based on a key observation: at temperature T, a system transits

τ = (kT/ħ) t

states in a (proper) time t, in a sense that is made precise below. The quantity τ was introduced in [13, 14] with different motivations, and called

==endquote==

http://arxiv.org/abs/1302.0724

Hal M. Haggard, Carlo Rovelli

(Submitted on 4 Feb 2013)

The zeroth principle of thermodynamics in the form "temperature is uniform at equilibrium" is notoriously violated in relativistic gravity. Temperature uniformity is often derived from the maximization of the total number of microstates of two interacting systems under energy exchanges. Here we discuss a generalized version of this derivation, based on informational notions, which remains valid in the general context. The result is based on the observation that the time taken by any system to move to a distinguishable (nearly orthogonal) quantum state is a universal quantity that depends solely on the temperature. At equilibrium the net information flow between two systems must vanish, and this happens when two systems transit the same number of distinguishable states in the course of their interaction.

5 pages, 2 figures

Notice that in the second paragraph of page 1 a distinction is made between two kinds of temperature--relativistic temperature labels the equivalence class of all systems which are in equilibrium with each other

( a kind of "zeroth law" temperature) and there is the temperature as measured by an ordinary thermometer.

This is a place where the paper may need further elucidation.

As I would paraphrase the following passage: thermal time is essentially a universal version of time that reconciles and unifies all those different clocks running at different temperatures. That is what equation (4) on page 1 is saying:

τ = (kT/ħ) t

Here is the context.

==quote 1302.0724, page 1==

The core idea is to focus on histories rather than states. This is in line with the general idea that states at fixed time are not a convenient handle on general relativistic mechanics, where the notion of process, or history, turns out to be more useful [12]. Equilibrium in a stationary spacetime, namely the Tolman law, is our short-term objective, but our long-term aim is understanding equilibrium in a fully generally covariant context, where thermal energy can flow also to gravity [13–15], therefore we look for a general principle that retains its meaning also in the absence of a background spacetime.

We show in this paper that one can assign an information content to a history, and two systems are in equilibrium when their interacting histories have the same information content. In this case the net information flow vanishes, and this is a necessary condition for equilibrium. This generalized principle reduces to standard thermodynamics in the non-relativistic setting, but yields the correct relativistic generalization.

This result is based on a key observation: at temperature T, a system transits

τ = (kT/ħ) t

states in a (proper) time t, in a sense that is made precise below. The quantity τ was introduced in [13, 14] with different motivations, and called

*thermal time*. Here we find the physical interpretation of this quantity: it is time measured in number of elementary “time steps”, where a step is the characteristic time taken to move to a distinguishable quantum state. Remarkably,**this time step is universal at a given temperature**. Our main result is that two systems are in equilibrium if during their interaction they cover the same number of time steps...==endquote==

http://arxiv.org/abs/1302.0724

**Death and resurrection of the zeroth principle of thermodynamics**Hal M. Haggard, Carlo Rovelli

(Submitted on 4 Feb 2013)

The zeroth principle of thermodynamics in the form "temperature is uniform at equilibrium" is notoriously violated in relativistic gravity. Temperature uniformity is often derived from the maximization of the total number of microstates of two interacting systems under energy exchanges. Here we discuss a generalized version of this derivation, based on informational notions, which remains valid in the general context. The result is based on the observation that the time taken by any system to move to a distinguishable (nearly orthogonal) quantum state is a universal quantity that depends solely on the temperature. At equilibrium the net information flow between two systems must vanish, and this happens when two systems transit the same number of distinguishable states in the course of their interaction.

5 pages, 2 figures

Notice that in the second paragraph of page 1 a distinction is made between two kinds of temperature--relativistic temperature labels the equivalence class of all systems which are in equilibrium with each other

( a kind of "zeroth law" temperature) and there is the temperature as measured by an ordinary thermometer.

This is a place where the paper may need further elucidation.

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